Waveguide taper of minimum length

ABSTRACT

A low-cost waveguide taper for interconnecting two circular waveguides which differ substantially in size is constructed from a plurality of reinforced, thin-walled conical sections having predetermined taper angles and axial lengths to minimize the effects of spurious modes generated at the junctions of the conical sections.

I Unlted States Patent 1 3,569,871

[72] Inventor Kiyo Tomiyasu OTHER REFERENCES Scot, Unger, CircularWaveguide Taper of improved Design, Bell 1 PP 754,700 System TechnicalJournal, Vol. 37, No. 4, July 1958, Pp. 899, 1 Filed 1968 903-906 and909 relied on $33-34 [45] Patented Mar. 9, 1971 P E P IL G I G 2 metricCom an rzmary xammerau ens er [73] Asslgnee en m p y An0rneys- Frank A.Paul, John F. Aherrl, Richard R.

, Brainard, Louis A. Moucha, Frank L. Neuhauser, Oscar B. [54] WAVEGUIDETAPER 0F MINIMUM LENGTH Waddell and Melvin M. Goldenberg 7 Claims, 2Drawing Figs.

[52] U.S.Cl. 333/34, 333/98 [51] Int.Cl "01p 1/16, HOlp 5/00 [50] Fieldof Search 333/34, 95, BS A lonhcost waveguide tape!- f interconnecting98-98 (M) two circular waveguides which differ substantially in size isR I CM constructed from a plurality of reinforced, thin-walled conical[56] 6 cream I sections having predetermined taper angles and axiallengths UNITED STATES PATENTS to minimize the effects of spurious modesgenerated at the 3,050,701 8/1962 Tang 333/34 junctions of the conicalsections,

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WAVEGUIDE TAPER F MINIMUM LENGTH My invention relates to a waveguidecomponent for interconnecting two circular waveguides which differsubstantially in size and method of fabrication thereof, and inparticular, to a waveguide taper of minimum length for interconnecting a2.25-diameter input waveguide to an oversize 29.7-inch diameter outputwaveguide adapted for propagating the TEK, mode at X-band frequency. Theinvention herein described was made in the course of or under a contractAf30 (602) 3810 with the Department of the Air Force.

Waveguides are conventionally employed for the propagation of lower owerlevel signals in the microwave frequency band, that is, for thepropagation of communication-type signals. Recently, it has beensuggested that waveguides may also be utilized as low-loss, highefficiency transmission devices for transmission of bulk electric power.The use of waveguides for the transmission and control of very highaverage power at C.W. microwave frequency requires the use of oversizewaveguides to obtain a low-loss transmission line. It is evident thatthe transmission of bulk power in the order of watts of power through awaveguide may cause considerable heating thereof unless the waveguideattenuation is reduced by approximately four orders of magnitude ascompared to the attenuation characteristics of conventional sizewaveguides. The reduced attenuation, in the order of 2.1 X 10- db. perfoot, is obtained for the transmission of power in the IE5, mode atX-band frequency in an oversize circular aluminum waveguide of 29.7-inchdiameter.

Although the use of oversize waveguides is feasible for the transmissionof bulk power at C.W. microwave frequencies, the application may belimited by other waveguide components in the microwave system. The inputend of the microwave system comprises a source for generating the bulkpower microwaves and an input waveguide connected to such source. Awaveguide device, commonly described as a waveguide taper, is utilizedto interconnect the input waveguide to the oversize waveguide utilizedin the transmission of the microwaves. In the case of propagation of theTE mode at X-band (5,200 to 10,900 MI-Iz.), and in particular, operationat a frequency of 8,3500 MHz, an oversize circular waveguide having aninner diameter of 29.7 inches has been found to have suitablecharacteristics such as low conductivity losses. The diameter of theinput waveguide is governed by the size of the TE mode transducer at theinput thereof, and at X-band such transducers have diameters of 1.3 to2.8 inches. A suitable transducer has a diameter of 2.25 inches. Thus,the waveguide taper device must be adapted for interconnectingwaveguides having diameters of 2.25 and 29.7 inches. A waveguide tapersuitable for this application has a continuously variable taper toprovide desired low mode conversion, but it has a minimum length ofapproximately ft. The fabrication costs of such a long, continuouslyvariable taper are excessive. Thus, in order to have bulk powertransmission of microwaves economically feasible, it is necessary toprovide a minimum length waveguide taper for interconnecting twocircular waveguides differing substantially in size, having low modeconversiontlosses, and capable of fabrication economi- .cally.

Therefore, one of the principal objects of my invention is to provide awaveguide taper of minimum length for interconnectingt-wo circularwaveguides differing substantially in size.

A further object of my invention is to construct the waveguide taperfrom a plurality of conical waveguide sections which provide interlacedpairs of mode-converting junctions having a canceling effect on thespurious modes generated at such junctions.

Briefly stated, my invention is a waveguide taper constructed from aplurality of thin wall conical waveguide sections. For the particularapplication wherein the waveguide taper interconnects an oversizecircular waveguide to a small diameter input waveguide, four differenttaper angles are employed. For ease of fabrication, each conical sectionis further comprised of two to four sections providing a total of 12conical sections. Adjacent sections are connected by flanges, and

stiffening rings are utilized to assure circularity of cross section ofeach waveguide section. The larger diameter waveguide sections arefabricated by rolling aluminum sheet metal into the desired conicalshape and longitudinal welding of such sections. The sections areprecisely aligned by optical means prior to being connected by means ofthe flanges.

The features of my invention which I desire to protect herein arepointed out with particularity in the appended claims. The inventionitself, however, both as to it organization and method of operation,together with further objects and advantages thereof, may best beunderstood by reference to the following description taken in connectionwith accompanying drawing, wherein like parts in each of the severalFIGS. are indentified by the same reference character and wherein:

FIG. 1 is a side view of the waveguide taper constructed in accordancewith my invention; and

FIG. 2 is a perspective view, partly in section, of the largest diametertaper section and section of the oversize circular waveguide connectedthereto. 1

Referring now in particular to FIG. 1, there is shown my waveguide taperstructure interconnecting a small diameter input circular waveguide 7with an oversize circular waveguide 8. The waveguide taper comprisesfour conical sections each indicated as a whole by numerals 3, 4, 5 and6, each section having a different taper angle varying from the largestangle at the small diameter end to the smallest taper angle at the largediameter end of the waveguide taper. Each section is further comprisedof a plurality of short length, conical waveguide sections for purposesof reducing the fabrication costs. My waveguide taper device can befabricated from only four separate sections, but an appreciably highercost than by my preferred low-cost method of fabrication utilizing theshort length sections to be described hereinafter. Obviously, mywaveguide taper can even be constructed from a single piece of metal butat such high cost that it would be economically unfeasible forapplication in bulk power transmission. Since one of the objects of myinvention is to provide a low-cost taper device, a waveguide tapercomprising a plurality of short length, conical sections hereinafterdescribed is one aspect of my invention. As is well known in thewaveguide art, mode conversion losses are caused by spurious orundesired modes generated at waveguide junctions having abrupt changesin taper angle. Thus, another aspect of my invention is the use of fourconical sections providing two pairs of mode conversion junctions whichare interlaced (cascaded) such that the first and third junction effectsand second and fourth junction effects each cancel as a pair. The first(cone-cone junction 9 is the junction of conical sections 3 and 4, thesecond (conecone) junction 10 is the junction of conical sections 4 and5, the third (cone-cone) junction 11 is the junction of conical sections5 and 6, and the fourth (cone-circular waveguide) junction 12 is thejunction of conical section 6 and the oversize circular waveguide 8.

The dimension of the large diameter end of my waveguide taper is equalto the diameter of the oversize aluminum waveguide 8. The diameter ofwaveguide 8 is determined approximately by factors such as attenuation,power capacity and waveguide heating. For the dominant (desired) mode ofpropagation, TES}, at a frequency of 8350 MHz., and desiredcharacteristics of attenuation 2.1 X 10- db./ft., maximum power capacity2.34 X l0 1 k watts where k =waveguide conductivity relative to copper,and waveguide surface heating =1 watt/ft.2, the approximate waveguidediameter is 30 inches. The exact dimension of waveguide 8 is determinedby considerations of undesired resonances near the cutoff frequency ofthe highest order modes which may be generated by the junction andpropagated in the oversize waveguide. For the particular case of TEbeing the dominant mode of propagation, the TEE and TESL- modes mayproduce the undesired resonances. A diameter of 29.7 inches for theoversize circular waveguide 8 and operating frequency of 8350 MHz.

1 percent and the T155 mode being above cutoff by approximately 4percent thereby preventing the propagation of the T125 mode, and toprovide for the TE; mode waveguide wavelength which is not excessivelylong and a wave impedance which is not excessively high. The inputwaveguide 7 is assumed to have a diameter of 2.25 inches for theparticular microwave system herein described. Thus, the particularwaveguide taper device constructed in accordance with my invention isadapted to connect a 2.25-inch diameter input waveguide to a 29.7-inchdiameter oversize waveguide supporting a TE mode at X-band.

The essential data for developing a waveguide taper comprising multiplecone sections are the magnitude and phase of the mode conversioncoefficients between the incident TE; mode and the spurious TEE modes.Although mode conversion results in many spurious modes being generatedat the four junctions 9, 10, 11, 12 of my waveguide taper, the mode ofgreatest concern is the TEg since its amplitude is the largest of allthe spurious modes.

By assuming that (a) it is the change in phase from curvature at ajunction which generates the higher order modes, and (b) the boundaryconditions are matched, it can be shown for graphical considerationsthat the mode coupling C between the "FE? and T53; modes isapproximately where A is the change in half-cone angle of the taper inradians, and D is the diameter at the junction. |C |is the modeconversion amplitude or magnitude of the mode coefficient. The phase ofthe mode conversion coefficient is 31/2 for small values of A0.

A basic design principle of a multi-conical taper is that the complexsum of all the mode conversions occuring at the junctions between theadjacent cones( and cone-circular waveguide) add to a sufficiently smallvalue within the frequency band of interest. In order to obtain thiscomputation, the differential phase constant AB between the TE and TBSmodes must be known as a function of diameter within the the taper. Thedifferential phase constant, also known as the differential phasevelocity or phase shift between the desired TE mode and the undesiredhigher order T155, modes is calculated from the following equations:

- radians/length degrees/length wherein his the operating frequency freewavelength;

A is the cutoff frequency wavelength of the TEE, mode,

equal to 0.82 D, D is the waveguide diameter;

space A is the cutofi frequency wavelength of the undesired higher orderT53, mode,

M is waveguide wavelength of the TE mode in waveguide with diameter D;and

A, is a waveguide wavelength of the TE? mode in waveguide with diameterD.

By the use of equations l) and (4), a waveguide taper having a length of208 inches (approximately 17% feet) comprising 12 conical sections withhalf-taper angles from 1 23.5 to 7 44.2 is obtained. The dimensions of12 taper sections comprising my waveguide taper device are as follows.

Wall Inside diam- Halt thicketer range, Length, taper ness, inchesinches angle inches Section 3a 2. 250-4. 600 11.50 744. 2 0. 3b 4.600-9. 926 19. 602 744. 2 3/16 3c 9. 926-15. 100 19.050 744. 2 0.250 15.100-17. 750 15. 145 5 0. 032 17. 750-20. 400 15. 145 5 0. 032 20.400-22. 250 17. 750 259 0. 032 22. 250-24. 100 17. 750 259 0.032 24.100-25. 950 17. 750 259 0. 040 25. 950-26. 887 19. 307 123.5 0. 040 26.887-27. 825 19. 307 123. 5' 0. 040 27. 825-28. 762 19. 307 123. 5 0. 04028. 762-29. 700 19. 307 123. 5 0. 040

The junctions 9, 10, 11 and 12 generate substantially identicalamplitudes of the TB; mode and the differential phase difference betweenadjacent junctions is 90. The two pairs of junctions 9, 10 and 11, 12are interlaced such at the first and third junctions (9, 11) are 1rradians apart in terms of the beat wavelength of the TE and T modes, andthe second and fourth junctions (10, 12) are also 11' radians apart andstaggered 90 from the first pair. This interlacing or cascading resultsin the first and third mode converting junctions cancelling as a pairthereby minimizing TE and TEf, mode of conversions (i.e., minimizing theloss of power to the T133 mode an d maximizing the desired TEg modeofpropagation.) and also resulting in a minimum length of waveguidetaper. Although the phase of the second pair ofjunctions 10, 12, is aquadrature (i.e. 90 staggered to that of the first pair, this feature isnot essential since the mode cancellation is achieved by pairsofjunctions.

Cover flanges 13 are utilized to connect adjacent conical sectionstogether, and such flanges are fastened on the ends of the conicalsections by any convenient means such as bonding, or the use of epoxy.Circular stiffening rings 14 are employed on the outer conical surfacesfor assuring circularity of the respective conical sections. The numberof stiffening rings utilized with each section is determined by thetolerances defined for the waveguide taper. As an example, onestiffening ring was used with section 4a, and the surface thereof wastrue to within 10.005 inch in circularity and straightness relative to aperfect cone.

The nine larger diameter conical sections (from 4a to 6b) thin wallmembers and are fabricated by the longitudinal welding of rolledaluminum sheet metal. The smallest diameter conical section 3a providesa continuously variable taper angle to blend into the 2.25-inch diameterinput waveguide, and this blend has a radius of approximately 24 inches.The constant flare angle produced by the continuously variable taperangle prevents the generation of any higher order modes and thus thejunction of section 3 and the input waveguide 7 is not considered to amode conversion junction. Section 3a is electroformed whereas the otherthicker wall sections 3b and 3c are machined. The specific l2-sectionwaveguide taper hereinabove described has been tested and found to meetthe various specifications hereinabove described including that of lowfabrications costs, light weight and acceptable electricalcharacteristics including that of negligible mode conversion losses asmeasured by a spinning dipole mode analyzer technique whereby thegreatly oversize circular waveguide 8 is capable of the transmission ofmicrowave power several orders of magnitude above that of conventionalwaveguides. Thus, the waveguide taper hereinabove described iscompatible with the low loss transmission line produced by the oversizewaveguide. In particular, in my specific 208-inch length taper thestrongest higher order modes detected, the T153 TE and TE; modes, areweaker than 20 db. below the TEf; mode. The length dimensions of thefour subdivided sections 3, 4, 5, 6 are indicated on FIG. 1. The largestdiameter section 6a, and its flanged connection to the oversize circularwaveguide 8 is illustrated in FIG. 2.

The waveguide taper is fabricated by the following method. The smallestdiameter section 3a is fabricated by employing an electroforming processand the next sections'3b and 3c are fabricated by machining (boring) rawaluminum stock. The nine larger diameter sections are fabricated byrolling thin aluminum sheet metal (0.032 and 0.040-inch thickness) intothe desired conical shapes and longitudinal butt-welding of suchthin-wall sections 4a to 6d. A special arc-welding fixture was built forobtaining the longitudinal welds. Successful longitudinal welds producedby the relatively low-cost special arcwelding fixture are limited toapproximately 24 inches in length, since the thin aluminum sheet metalmust be welded under very carefully controlled conditions in order toobtain conical sections having the desired preciseness in circularity ofcross section. It is this welding limitation which limits the maximumaxial length of each taper section. Obviously, longer length sectionscan be produced by employing higher cost welding fixtures, but thiswould then negate one of the objects of my invention, that of providinga low-cost fabrication method.

After the conical sections have been welded, the stiffening rings areslid onto desired axial locations of the various sections. As indicatedin FIG. 1, one stiffening ring 14 is used on small diameter sections 3b, 30, 4a, 4b, 5a, 5b, 5c, and two stiffening rings are used on largediameter sections 6a, 6b, 6c, 6d. The stiffening rings are approximatelyequally spaced from each other and from the section ends. After thestiffening rings are in place, the cover flanges 13 are slid onto theends of each section. A special epoxying fixture is utilized forfastening the flanges and stiffening rings onto the waveguide tapersections. The epoxying fixture is used to align the flanges andstiffening rings on the taper section, and after alignment, epoxy, isused to bond the flanges and rings onto each taper section.

After the conical sections have been completely fabricated, they'areassembled into a single structure. A long support structure is utilizedfor aligning the 12 conical sections, and for holding and aligning the17.5 foot long taper with the oversize circular waveguide and inputwaveguide. The support structure is diagonally braced for increasedrigidity and is bolted to the ground for stability. An optical techniqueis used in the alignment process including a pinpoint diameter lightsource fastened one-half inch radially outward on a flange at one end ofthe waveguide assembly and a pinpoint diameter peep hole similarlyfastened outward on a flange at the other end thereof. An 8 inch longtapered piece of metal made from sheet aluminum having endsthree-eighths inch and five-eighths inch wide, respectively, is placedon each intervening flange, and by noting the position of the taper thatwould decrease by one-half the light seen through the peep hole, theposition of the largest diameter flange interconnecting the taper andoversize waveguide is determined.

An average optical axis was established that permits flange alignment towithin the range of the adjusting screws on leveling fixtures located ontop of the support structure. The flanges interconnecting sections 5b,5c and 6a of the waveguide taper are then bolted together and alignedwith the average optical axis. Thereafter, the alignment of theremaining sections is adjusted by the leveling fixtures to make themating flanges parallel after which the flanges are bolted together. Inthe final assembly, all of the flanges were aligned within :3/64 inchand :3/128 inch the horizontal and vertical planes, respectively.

From the foregoing description, it can be appreciated that my inventionmake available an improved minimum length waveguide taper device andlow-cost method of fabrication thereof. The particular 17.5 foot lengthis a substantial reduction in length from a 30 foot continuouslyvariable taper which exhibits comparable electrical characteristics. Thewaveguide taper is adapted for interconnecting waveguides ofsubstantially different diameter sizes, and in particular, is especiallyadapted for interconnecting a small diameter input waveguide to agreatly oversize circular waveguide suitable for transmitting powerlevels at X-band frequencies of several orders of magnitude higher thanthat of conventional size waveguides. The waveguide taper may alsofindapplication as a broadband radiating element or radiating aperturehaving negligible phase and amplitude distortion. Although theparticular waveguide taper described hereinabove may be fabricated byother means, the other methods are all inherently much more expensivethereby rendering it economically unfeasible for use of such componentin a microwave system for transmitting bulk power. The use of aplurality of reinforced thin-walled waveguide taper sections results ina low-cost fabrication method which provides the desired dimensions andtolerances and obtains acceptable electrical characteristics includingthose of negligible mode conversion and the further advantage of beinglightweight.

Having described the waveguide taper structure and method of fabricationin accordance with my invention, it is believed obvious that othermodifications and variations of my invention are possible in the lightof the above teachings. For example, a more expensive welding jig can beutilized for welding seams greater than 24 inches in length and therebyutilizing a smaller number than 12 for the sections comprising my 17.5foot length taper. Further, the stiffening rings may be omitted byutilizing thicker walls in the waveguide taper sections. However, thesemodifications result in either or both a more expensive fabricationsmethod and structure and also a greater weight structure. Thus, sinceone of the objects of the invention is to provide a low-cost,lightweight structure, it is seen that the use of a plurality of shortlength, reinforced, thinwalled conical sections is the preferredembodiment. My invention is thus defined by the following claimsv Iclaim:

1. A waveguide taper of minimum length for interconnecting two circularwaveguides differing substantially in diameter size comprising:

12 conical waveguide sections connected in order of increasingdiameters, said sections having selected axial lengths and fourdifferent taper angles for minimizing the generation of spurious modesat the junctions of different taper angles, the larger diameter conicalsections comprising thin-wall members;

pairs of alternate junctions being interlaced and the junctions of eachpair being 71 radians apart in terms of the beat wavelength of adominant and spurious mode of propagation to thereby substantiallycancel the effect of the spurious mode and provide a waveguide taper oflength substantially shorter than a waveguide taper having acontinuously variable taper wherein both waveguide tapers are adaptedfor propagating the same dominant mode at the same frequency and havingcomparable electrical characteristics; and

the four sections of largest diameter have a first common taper angle,the next three sections have a second common taper angle, the next twosections have a third common taper angle, and the three smallestdiameter sections have a fourth common taper angle.

2. The waveguide taper of minimum length set forth in claim 1 whereinthe smallest diameter section has a continuously variable taper angleterminating in the fourth common taper angle whereby four junctions ofdifferent taper angles are provided to form two interlaced pairs of thealternate junctions.

3. The waveguide taper of minimum length set forth in claim 2 wherein:

said waveguide taper has minimum and maximum inside diameters of 2.250and 29.700 inches, respectively; and

said waveguide taper has a total length of 208 inches which issubstantially shorter than a comparable continuously variable taperhaving similar electrical characteristics and a minimum total length of30 feet wherein the waveguide tapers are adapted for propagating the TEXmode at X- band frequency with negligible mode conversion losses.

4. The waveguide taper of minimum length set forth in claim 3 whereinthe first common taper is 1 23.5, the second common taper angle is 2 59,the third common taper angle is 5, and the fourth common taper angle is7 44.2.

5. The waveguide taper minimum length set forth in claim 4 wherein thefour sections of largest diameter each have an axial length of 19.307inches, the next three sections each have an axial length of 17.750inches, and the next two sections each have an axial length of 15.145inches.

6. The waveguide taper of minimum length set forth in claim wherein thefive sections of largest diameter each have a wall thickness of 0.040inch and the next four sections each have a wall thickness of0.032 inch.

7. A waveguide taper of minimum length for interconnecting two circularwaveguides differing substantially in diameter size comprising:

12 conical waveguide sections connected in order of increasingdiameters, said sections having selected axial lengths and fourdifferent taper angles for minimizing the generation of spurious modesat the junctions of different taper angles, the larger diameter conicalsections comprising thin-wall members; and

pairs of alternate junctions being interlaced and the junctions of eachpair being 1r radians apart in terms of the beat wavelength of adominant and spurious mode of propagation to thereby substantiallycancel the effects of the spurious mode and provide a waveguide taper oflength substantially shorter than a waveguide taper having acontinuously variable taper wherein both waveguide tapers are adaptedfor propagating the same dominant mode at the same frequency and havingcomparable electrical characteristics.

1. A waveguide taper of minimum length for interconnecting two circularwaveguides differing substantially in diameter size comprising: 12conical waveguide sections connected in order of increasing diameters,said sections having selected axial lengths and four different taperangles for minimizing the generation of spurious modes at the junctionsof different taper angles, the larger diameter conical sectionscomprising thin-wall members; pairs of alternate junctions beinginterlaced and the junctions of each pair being pi radians apart interms of the beat wavelength of a dominant and spurious mode ofpropagation to thereby substantially cancel the effect oF the spuriousmode and provide a waveguide taper of length substantially shorter thana waveguide taper having a continuously variable taper wherein bothwaveguide tapers are adapted for propagating the same dominant mode atthe same frequency and having comparable electrical characteristics; andthe four sections of largest diameter have a first common taper angle,the next three sections have a second common taper angle, the next twosections have a third common taper angle, and the three smallestdiameter sections have a fourth common taper angle.
 2. The waveguidetaper of minimum length set forth in claim 1 wherein the smallestdiameter section has a continuously variable taper angle terminating inthe fourth common taper angle whereby four junctions of different taperangles are provided to form two interlaced pairs of the alternatejunctions.
 3. The waveguide taper of minimum length set forth in claim 2wherein: said waveguide taper has minimum and maximum inside diametersof 2.250 and 29.700 inches, respectively; and said waveguide taper has atotal length of 208 inches which is substantially shorter than acomparable continuously variable taper having similar electricalcharacteristics and a minimum total length of 30 feet wherein thewaveguide tapers are adapted for propagating the TE01 mode at X-bandfrequency with negligible mode conversion losses.
 4. The waveguide taperof minimum length set forth in claim 3 wherein the first common taper is1* 23.5'', the second common taper angle is 2* 59'', the third commontaper angle is 5*, and the fourth common taper angle is 7* 44.2''. 5.The waveguide taper minimum length set forth in claim 4 wherein the foursections of largest diameter each have an axial length of 19.307 inches,the next three sections each have an axial length of 17.750 inches, andthe next two sections each have an axial length of 15.145 inches.
 6. Thewaveguide taper of minimum length set forth in claim 5 wherein the fivesections of largest diameter each have a wall thickness of 0.040 inchand the next four sections each have a wall thickness of 0.032 inch. 7.A waveguide taper of minimum length for interconnecting two circularwaveguides differing substantially in diameter size comprising: 12conical waveguide sections connected in order of increasing diameters,said sections having selected axial lengths and four different taperangles for minimizing the generation of spurious modes at the junctionsof different taper angles, the larger diameter conical sectionscomprising thin-wall members; and pairs of alternate junctions beinginterlaced and the junctions of each pair being pi radians apart interms of the beat wavelength of a dominant and spurious mode ofpropagation to thereby substantially cancel the effects of the spuriousmode and provide a waveguide taper of length substantially shorter thana waveguide taper having a continuously variable taper wherein bothwaveguide tapers are adapted for propagating the same dominant mode atthe same frequency and having comparable electrical characteristics.